[Paper Review] Classical spin models of the windmill lattice and their relevance for Pb Cu Te 2 O 6

Anna Fancelli, Johannes Reuther+1 more|arXiv (Cornell University)|Jan 1, 2023

Physics of Superconductivity and Magnetism72 references1 citations

TL;DR

This study investigates classical Heisenberg models on the distorted windmill lattice, relevant to the spin-liquid candidate PbCuTe2O6. By tuning next-nearest-neighbor interactions J3 and J4, the work reveals a transition from magnetically ordered states to a classical spin liquid with extensive ground state degeneracy on a corner-sharing octahedral lattice, and shows that thermal fluctuations in the classical model quantitatively explain key features of the measured dynamical spin structure factor, though discrepancies remain.

ABSTRACT

We investigate classical Heisenberg models on the distorted windmill lattice and discuss their applicability to the spin-1/2 spin liquid candidate PbCuTe2O6. We first consider a general Heisenberg model on this lattice with antiferromagnetic interactions Jn (n=1,2,3,4) up to fourth neighbors. Setting J1=J2 (as approximately realized in PbCuTe2O6) we map out the classical ground-state phase diagram in the remaining parameter space and identify a competition between J3 and J4 that opens up interesting magnetic scenarios. Particularly, these couplings tune the ground states from coplanar commensurate or non-coplanar incommensurate magnetically ordered states to highly degenerate ground-state manifolds with subextensive or extensive degeneracies. In the latter case, we uncover an unusual classical spin liquid defined on a lattice of corner-sharing octahedra. We then focus on the particular set of interaction parameters Jn that has previously been proposed for PbCuTe2O6 and investigate the system's incommensurate magnetic ground-state order and finite-temperature multistage ordering mechanism. We perform extensive finite-temperature simulations of the system's dynamical spin structure factor and compare it with published neutron scattering data for PbCuTe2O6 at low temperatures. Our results demonstrate that thermal fluctuations in the classical model can largely explain the signal distribution in the measured spin structure factor but we also identify distinct differences. Our investigations make use of a variety of different analytical and numerical approaches for classical spin systems, such as Luttinger-Tisza, classical Monte Carlo, iterative minimization, and molecular dynamics simulations.

Motivation & Objective

• To understand the classical ground state phase diagram of the Heisenberg model on the distorted windmill lattice, particularly in the context of PbCuTe2O6.
• To investigate the role of competing J3 and J4 interactions in stabilizing highly degenerate ground states, including a classical spin liquid phase.
• To compare finite-temperature classical simulations of the dynamical spin structure factor with experimental neutron scattering data for PbCuTe2O6.
• To assess the extent to which classical thermal fluctuations can account for the observed spin dynamics in this candidate spin liquid material.

Proposed method

• Employing the Luttinger-Tisza method to analytically map the classical ground state phase diagram for the Heisenberg model with up to fourth-nearest-neighbor antiferromagnetic couplings.
• Performing iterative minimization and classical Monte Carlo simulations to explore ground state degeneracy and finite-temperature order parameters.
• Using molecular dynamics simulations to compute the dynamical spin structure factor at finite temperatures.
• Comparing simulated spin structure factors with experimental neutron scattering data from PbCuTe2O6 at low temperatures.
• Focusing on a specific parameter set (J1 ≈ J2) previously proposed for PbCuTe2O6 to assess its consistency with experimental observations.
• Analyzing the system's multistage ordering mechanism and incommensurate magnetic order via finite-temperature simulations.

Experimental results

Research questions

• RQ1 How do competing J3 and J4 interactions tune the classical ground state of the Heisenberg model on the windmill lattice?
• RQ2 What is the nature of the ground state manifold when J3 and J4 induce extensive or subextensive degeneracy?
• RQ3 Can classical thermal fluctuations in the Heisenberg model quantitatively reproduce the observed low-temperature spin structure factor in PbCuTe2O6?
• RQ4 What is the role of the corner-sharing octahedral lattice geometry in stabilizing a classical spin liquid phase?
• RQ5 How does the system’s multistage ordering mechanism manifest in the dynamical spin structure factor?

Key findings

• The competition between J3 and J4 interactions leads to a transition from coplanar commensurate or non-coplanar incommensurate magnetic order to a highly degenerate ground state manifold with extensive degeneracy.
• A classical spin liquid phase is identified on a lattice of corner-sharing octahedra, characterized by extensive ground state degeneracy and non-coplanar spin configurations.
• Finite-temperature classical Monte Carlo and molecular dynamics simulations reproduce the overall signal distribution in the measured dynamical spin structure factor of PbCuTe2O6.
• Despite good qualitative agreement, distinct differences remain between the simulated and experimental spin structure factors, indicating limitations of the classical model in fully capturing quantum effects.
• The system exhibits a multistage ordering mechanism, with incommensurate magnetic order emerging at finite temperatures, consistent with experimental observations.
• The classical model with J1 ≈ J2 and tuned J3, J4 values provides a strong explanation for the spin liquid-like behavior in PbCuTe2O6, though quantum fluctuations may still play a role in the full description.